Historical ERP: A Poor Estimator of Future ERP

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1 Historical ERP: A Poor Estimator of Future ERP The equity risk premium or ERP (often interchangeably referred to as the market risk premium) is defined as the extra return investors demand for investing in stocks rather than investing in risk-free securities. Estimating the ERP is one of the most important decisions the valuation practitioner must make in developing a discount rate. In one recent paper, the authors conclude that the ERP is almost certainly the most important variable in finance. 1 In general, for capital markets to work, stocks should produce on average higher returns than bonds over the long term. This risk-return relationship should be particularly true when stocks are compared to government bonds that (ostensibly) cannot default. 2,3 1 Richard C. Grinold, Kenneth K. Kroner, and Laurence B. Siegel, A Supply Model of the Equity Premium, Rethinking the Equity Risk Premium, edited by P. Brett Hammond Jr., Martin L. Leibowitz, and Lawrence B. Siegel, The Research Foundation of CFA Institute (2011): Robert D. Arnott, Equity Risk Premium Myths, in Rethinking the Equity Risk Premium, edited by P. Brett Hammond Jr., Martin L. Leibowitz, and Lawrence B. Siegel, The Research Foundation of CFA Institute (2011): The stock market does not always outperform U.S. government bonds. For example, in the 20-year period ending December 2012, the S&P 500 Index returned 8.22% per year and 20-year U.S. Treasuries returned 8.59% per year (geometric, or compound, averages).

2 Historical ERP Is a Poor Estimator of Future ERP The equity risk premium or ERP (often interchangeably referred to as the market risk premium) is defined as the extra return investors demand for investing in stocks rather than investing in risk-free securities. Estimating the ERP is one of the most important decisions the valuation practitioner must make in developing a discount rate. In one recent paper, the authors conclude that the ERP is almost certainly the most important variable in finance. 1 In general, for capital markets to work, stocks should produce on average higher returns than bonds over the long term. This risk-return relationship should be particularly true when stocks are compared to government bonds that (ostensibly) cannot default. 2,3 A common way of estimating the U.S. ERP is to look at the historical relationship between stocks (typically represented by the S&P 500 Index) and 20-year U.S government bonds. ERP estimates derived in this fashion are commonly referred to as historical ERP, since they use historical data. For example, the ERP published on the back page of the SBBI Valuation Yearbook is calculated as the average difference in annual total returns of the S&P 500 Index and the annual income return of the 20-year U.S. government bond over prior (i.e., historical) periods. 4,5 This historical ERP is known as the long-horizon expected equity risk premium and is calculated using data from 1926-present. When we develop a cost of capital, it is presumably going to be used to discount future expected cash flows back to present value. Thus, cost of capital and all of its inputs should be forward looking, including the ERP. In this article, we examine whether an ERP estimate calculated as the historical average annual difference in returns on stocks and the risk-free security (e.g., as published in the SBBI Valuation Yearbook) is a good predictor of future performance differences between stocks and long-term U.S. government bonds. The evidence suggests that it is not a good predictor. Back Testing the Historical ERP In this article, we perform a simple back test of the historical ERP. Back testing can be thought of as using historical data to see whether a prediction (made in the past) actually came true. For example, if I had made a prediction in 2005 that the Philadelphia Phillies would win the World Series in 2009, we could easily back test that prediction since we know how the 2009 World Series ended: The Phillies didn t win (the Yankees did). My prediction was wrong. Oh, well. 1 Richard C. Grinold, Kenneth K. Kroner, and Laurence B. Siegel, A Supply Model of the Equity Premium, Rethinking the Equity Risk Premium, edited by P. Brett Hammond Jr., Martin L. Leibowitz, and Lawrence B. Siegel, The Research Foundation of CFA Institute (2011): Robert D. Arnott, Equity Risk Premium Myths, in Rethinking the Equity Risk Premium, edited by P. Brett Hammond Jr., Martin L. Leibowitz, and Lawrence B. Siegel, The Research Foundation of CFA Institute (2011): The stock market does not always outperform U.S. government bonds. For example, in the 20-year period ending December 2012, the S&P 500 Index returned 8.22% per year and 20-year U.S. Treasuries returned 8.59% per year (geometric, or compound, averages). 4 The back page of the Morningstar SBBI Valuation Yearbook also reports a supply side equity risk premium. The historical equity risk premium is the equity risk premium Morningstar uses to calculate the size premia published on the back page of the SBBI Valuation Yearbook. 5 The SBBI Valuation Yearbook is published annually by Morningstar (Chicago).

3 To back test the historical ERP, we followed a similar process. The historical ERP is supposed to be a prediction of the future performance of stocks relative to the risk-free security (in the U.S., the risk-free security is typically proxied for by a long-term U.S. government bond). If we know what the historical ERP prediction was in, say, 1945 (and we do!), we can compare that 1945 prediction to something else we know: how stocks actually performed relative to the risk-free security over, say, the 20-year period right after How did the 1945 ERP prediction pan out? Well, the 1945 historical ERP was 8.06%, but in the 20 years right after 1945 ( ), stocks outperformed the 20-year U.S. government bond by 12.23%. The ERP prediction underestimated the next 20 years performance of stocks relative to the risk-free security by 4.17% (12.23% %). 6,7,8 That s just the type of simple back testing analysis we did for this article. We pretended that the SBBI Valuation Yearbook was first published in 1946 (with data through Dec. 31, 1945) and calculated the historical ERP as it would have been calculated for a hypothetical 1946 Yearbook, 1947 Yearbook, 1948 Yearbook, and so on, until Now, to be clear, the SBBI Valuation Yearbook (Morningstar, Chicago) was actually first published in 1999 (with data through Dec. 31, 1998) we are just pretending that it was first published in 1946 in this article for the purpose of our ERP back testing experiment. Why did we stop the experiment with a 1993 Yearbook? Because a hypothetical 1993 SBBI Valuation Yearbook would have been published with a historical ERP calculated using data from The 20 years right after 1992 ( ) is the last time there was a full 20-year period ahead of it (2013 hasn t ended yet!). The table in Exhibit 1 provides an abbreviated summary of all the calculations made in this experiment. 6 Stocks are represented in ERP calculations here by the S&P 500 Index. Twenty-year U.S. government bonds are represented in ERP calculations by the income return of the SBBI long-term government bond series. The methodology and data used to calculate the historical ERP in this article match the methodology and data used to calculate the historical ERP as published on the back page of the Ibbotson SBBI Valuation Yearbook (Morningstar, Chicago). Calculated by Duff & Phelps. Source of underlying data: Morningstar EnCorr database. 7 The historical ERP as of Dec. 31, 1945, would have been calculated using data over the period Over that period, the S&P 500 Index had an arithmetic average annual return of 10.94% and the average annual income return of a long-term U.S. government bond was 2.88%. The historical ERP at the end of 1945 was therefore 8.06% (10.94% %). 8 From the S&P 500 Index had an annual performance of 13.84%, while 20-year U.S. government bonds had an annual performance of 1.61%. The difference is 12.23% (13.84% %). 9 We decided to start our analysis with a hypothetical 1946 SBBI Valuation Yearbook because that is the first year in which the historical ERP can be calculated using at least 20 years of data ( ). The historical ERP is measured as an average over time and is sensitive to the number of periods used (generally, the more, the better). Our selection of a minimum of 20 years is arbitrary. Nonetheless, 20 years may be a reasonable reflection of the duration of the projected cash flows for a firm.

4 Exhibit 1: Back Testing the Historical ERP (A) The solid red line in Exhibit 2 (B) The dashed black line in Exhibit 2 (B) - (A) Difference (see Exhibit 3) Historical ERP Actual Future Performance of stocks relative to the riskfree security over next 20 years Actual Future Performance - Historical ERP Hypothetical SBBI Yearbook: As Calculated Over Years: As Calculated Over Years: (B - A) 1946 SBBI Yearbook (8.06%) (12.23%) 12.23% % = -4.17% (underestimate) 1947 SBBI Yearbook (7.19%) (11.92%) 11.92% % = -4.73% (underestimate) 1948 SBBI Yearbook (7.03%) (13.18%) 13.18% % = -6.15% (underestimate) 1992 SBBI Yearbook (7.39%) (-1.02%) -1.02% % = 8.41% (overestimate) 1993 SBBI Yearbook (7.29%) (-0.37%) -0.37% % = 7.66% (overestimate) The solid red line in the graph in Exhibit 2 is the historical ERP as calculated over the periods (on the far left, 8.06%), , , etc., until the last ERP calculation is made over the period (on the far right, 7.29%). This line can be thought of as the prediction of how stocks would perform relative to the risk-free security in subsequent periods and is the same as (A) in Exhibit 1. This line is the historical ERP that would have been published in our hypothetical SBBI Yearbooks. The dashed black line in Exhibit 2 is the actual performance of stocks relative to 20-year U.S. government bonds in the 20-year periods after each of the ERP predictions, and is the same as (B) in Exhibit 1. For example, on the far left, the ERP prediction at the end of 1945 was 8.06%, and, in the 20 years that followed that prediction ( ), stocks outperformed the risk-free security by 12.23%. Again, the ERP prediction that year therefore underestimated the performance of stocks relative to the risk-free security over the subsequent 20 years by 4.17% (8.06% %). Alternatively, on the far right, the historical ERP was 7.29%, and, in the 20 years after 1992 ( ), stocks underperformed the risk-free rate by %. The ERP prediction that year therefore overestimated the performance of stocks relative to the riskfree security over the subsequent 20 years by 7.66% (7.29% - (-0.37%)). In short, when the solid red line (predicted performance) is below the dashed black line (actual performance) in Exhibit 2, the historical ERP underestimated (was lower than) the subsequent actual 20-year performance of stocks relative to U.S. government bonds. Conversely, when the solid red line is above the dashed black line, the historical ERP overestimated (was higher than) the subsequent actual 20-year performance of stocks relative to U.S. government bonds.

5 Exhibit 2: The Historical ERP Versus Actual Difference in Subsequent 20-Year Period in Stock s Performance Versus 20-Year U.S. Government Bonds Performance An alternative perspective of this analysis is provided in Exhibit In Exhibit 3, the difference between the historical ERP (the solid red line in Exhibit 1) and the subsequent performance of stocks over 20-year U.S. government bonds (the dashed black line in Exhibit 1) is plotted. This difference can be thought of as how accurate the historical ERP was in predicting subsequent stock performance relative to 20-year U.S. government bonds and is the same as (A) - (B) in the table in Exhibit 1. As can be seen in the graph in Exhibit 3, the annual historical ERP estimate has overestimated the subsequent 20-year performance of stocks relative to subsequent total returns on 20-year U.S. government bonds (the risk-free security ) since 1954 (and through the 1992 estimate). This suggests that the historical ERP may generally be on the high side. 10 Source of data used in Exhibit 3: Morningstar EnCorr Analyzer. Calculations by Duff & Phelps.

6 Exhibit 3: Difference Between the Historical ERP and (Subsequent 20-Year Performance of Stocks - Subsequent 20-Year Performance of 20-Year U.S. Government Bonds) The Perfect Foresight ERP? We then asked ourselves: If we had perfect foresight, what single ERP estimate could we have made in all years in our hypothetical SBBI Yearbooks that would have minimized the difference between our ERP prediction and the subsequent actual 20-year performance of stocks relative to long-term government bonds (in other words, been more accurate)? This single ERP turns out to be 4.67%. The dashed red line in Exhibit 4 represents the 4.67% ERP (used in all years ) minus the subsequent 20-year performance of stocks relative to long-term government bonds (the solid red line in Exhibit 4 is just a repeat of the line in Exhibit 3). Note that the dashed red line is generally closer to 0% than the solid red line, indicating that using 4.67% as the ERP estimate (rather than the historical ERP estimate, as indicated by the solid red line) would have been a better estimate of future performance of stocks relative to long-term government bonds. In other words, the difference between the prediction (ERP) and actual subsequent returns was smaller if we used 4.67% rather than the historical ERP). The conclusion is that if the SBBI Valuation Yearbook had been published since 1945 all the way through 1992, an ERP estimate of 4.67% (each and every year!) would have been an overall more accurate prediction of ERP than the actual historical ERP would have been!

7 Exhibit 3: Overestimates and Underestimates of Subsequent Relative Performance of Stocks and Long-Term Government Bonds Using the Historical ERP and Single ERP of 4.67% ( ) Possible Criticisms of this Analysis Now, there are valid criticisms of this analysis. For example, just as the historical ERP will change depending on what period it is measured over, the analysis in this article will also change depending on what period it is measured over. 11 In the previous examples, the first calculated historical ERP was for 1945, using data over (1945 is the first year for which at least 20 years of data are available to calculate an ERP), and using this 1945 start date resulted in a so-called perfect foresight ERP of 4.67%. However, if we had simply decided that we wanted at least 30 years of data to calculate a historical ERP, the first year a historical ERP could have been calculated is 1955, and the perfect foresight ERP that would result is 3.08%! This demonstrates how sensitive the results can be to the time period analyzed and the number of years used in each calculation. Another potential weakness of this analysis is that, just as the historical ERP takes time to stabilize (i.e., the more years of data used, the better), we only used 20-year periods of subsequent performance of stocks 11 The historical ERP is sensitive to the amount of time over which it is measured, and to the period over which it is measured. Morningstar states that A proper estimate of the equity risk premium requires a data series long enough to give a reliable average without being duly influenced by very good and very poor short-term returns, and When calculated using a long data series, the historical equity risk premium is relatively stable. Source: 2012 SBBI Valuation Yearbook (Morningstar, Chicago), page 59.

8 relative to long-term government bonds. The same argument that the more years of data used, the better could also be applied to this measurement. Conclusion To be clear: In these analyses, we are not saying that the historical ERP is not a useful clue in estimating the forward-looking ERP (it is!). Furthermore, in these analyses we are not attempting to calculate the true ERP, and thus we are not saying that the true ERP is 4.67% or even 3.08%. 12 In this analysis, we are merely trying to gauge (in a general way) whether the historical ERP is generally good at predicting the future relationship between stocks and the risk-free security. Is it generally high, low, or just right? Our analysis suggests that the historical ERP is not a very good predictor and that it tends to be on the high side. In other words, this analysis suggests that the historical ERP tends to overestimate the actual ERP in subsequent periods. Specifically, this analysis suggests that the historical ERP has overestimated the subsequent actual 20-year performance of stocks relative to long-term government bonds every year since This analysis provides additional evidence that suggests that the ERP is likely lower today than what might be indicated by using the average of historical realized risk premiums beginning in 1926, as published in the SBBI Valuation Yearbook. 13 A Modest Proposal in Regards to ERP Estimation There is no single universally accepted method for estimating the equity risk premium (ERP). Each ERP model has strengths and weaknesses. No ERP estimation model is a stand-alone model. Using any single model of ERP estimation in a vacuum can be problematic. Multiple ERP estimation models should be used when developing an ERP. 12 The likely range of the U.S. ERP over a full business cycle is 3.5%-6.0%. To learn more about the ERP, download a free copy of the article Duff & Phelps Decreases U.S. Equity Risk Premium Recommendation to 5.0%, Effective February 28, 2013 at 13 It is noted that the SBBI Valuation Yearbook includes an Appendix entitled Long-Horizon Equity Risk Premia, which reports the historical arithmetic ERP computed by starting (or ending) in any year selected by the user over the period 1926-present. For example, the 2013 Yearbook reports a 4.7% historical ERP for the 20-year period beginning in 1993 and ending in 2012.

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